Life support rooms require at least one Oxygen Recycler. It's also usually a good idea to build a Fire Extinguisher as well, but not necessary.
You can also place monitors and ordinary plants in life support rooms to help keep your technicians happy.

Rooms with more people in (like bars and residences, or high traffic corridors) tend to have less oxygen because there are more citizens breathing it in.

Rooms need to be physically attached to a structure with a life support room in order to be filled with oxygen.
All wall and door tiles have built-in ventilation ducts which allow oxygen to spread through them to adjacent rooms. Locking doors will do nothing to stop the spread of oxygen, but clicking on the room and selecting "Seal Oxygen" will cut off its oxygen flow and any citizens inside will slowly suffocate unless the room has breaches or open doors.
Large, well-populated bases frequently require far more than one Oxygen Recycler per 3 citizens. Remember to have your Technicians keep the recyclers running strong.

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